Comparison of various phased approaches for the constrained minimum-cost design of water distribution networks

In most cases, water system design is based on a demand forecast at the end of some planning horizon based on the final configuration of the system at that time. This design approach (aimed at designing all the network at a time) is incompliant with its actual development, which instead takes place in phases. As a consequence, in order to follow the network demand and layout growth in time, practitioners prefer to sub-divide the whole construction life into various time phases thus including the different phases of construction in the network design. This work is aimed at analyzing and comparing three different phased approaches for constrained minimum-cost design of water distribution networks: the single-phase design with demand feedback, the multi-phase design without demand feedback and the multi-phase design with demand feedback. The difference between the single-phase design and the multiphase design lies in the fact that whereas the former entails optimizing a single construction phase at a time, i.e. the current construction phase, the latter is based on the phasing of construction and then is aimed at optimizing the current construction phase and all the subsequent phases, included inside a certain temporal horizon, simultaneously. The demand feedback is here used as a pragmatic tool for updating the forecast at some specific time instant of the future demand growth: such an update is performed by setting the future demand growth equal to that really observed in the previous time phase. Alternatively, the predicted demand growth rate at the generic time instant can be kept equal to the value assumed at the time instant when the generic node appears, without taking account of the demand variation really observed in time in the node (absence of demand feedback). Applications to a real case study show that the multi-phase design with the demand feedback is the most reliable because it makes it possible to reduce the overall construction costs while attenuating the occurrence of pressure deficits in the various construction phases of the network. Optimal design for a single phase will virtually guarantee a sub-optimal solution over the long run.